Someone who solves problems is just that: a person who solves problems. To be a creative thinker is someone who thinks creatively, but what exactly does that mean?

The definition of creativity is a bit fuzzy, even for experts who study the subject. What is generally considered as “creative” are ideas which are both novel and useful.

Imagining a way to toast bread until it’s burnt to the point it disintegrates is a pretty unique idea, but not a very useful one. Likewise, coming up with an idea on how to use a gasoline engine to propel a vehicle forward is useful but not so much unique. For an idea to be truly creative it must be both unique and valuable.

By this definition of creativity you cannot really be a creative thinker unless you’re also solving a problem; an idea isn’t truly creative unless it’s valuable, which is another way of saying it solves some problem.

However, that doesn’t mean all creative thinkers necessarily start their thinking by identifying a problem to be solved. In many cases a creative idea comes as a result of an accident, an observation, or happenstance. But in each instance the person coming up with the idea is both solving a problem (valuable) and coming up with something novel (something nobody else in their “world” has come up with).

That is to say: it absolutely is possible to come up with a creative idea without explicitly thinking of problem. But in generating a creative idea you’ll be solving some type of problem.

You can be a problem solver without thinking creatively (a solution to the problem being solved may already be in existence). You can’t be a creative thinker without being a problem solver (being capable of coming up with ideas that are both unique and valuable).

The trick is to consistently be generating ideas that are unique and/or valuable. Those ideas don't necessarily need to solve a large or immediate problem. As Clayton Christensen writes in his book Competing Against Luck:

Even if a theory doesn’t apply to some particular application, it’s still valuable because knowing when a particular theory doesn’t help explain something will allow you to turn to others to find better answers."